Related papers: Discrete series L-packets for real reductive group…

The second author has recently introduced a new class of L-series in the arithmetic theory of function fields over finite fields. We show that the value at one of these L-series encode arithmetic informations of certain Drinfeld modules…

In 1979 Lusztig proposed a conjectural construction of supercuspidal representations of reductive p-adic groups, which is similar to the well known construction of Deligne and Lusztig in the setting of finite reductive groups. We present a…

The investigation of the role of finite groups in flavor physics and particularly, in the interpretation of the neutrino data has been the subject of intensive research. Motivated by this fact, in this work we derive the three-dimensional…

We show new properties of the Langlands correspondence for arbitrary tori over local fields. Furthermore, we give a detailed analysis of depth-zero characters of reductive p-adic groups, for groups that may be wildly ramified. We present…

L-convex sets are one of the most fundamental concepts in discrete convex analysis. Furthermore, the Minkowski sum of two L-convex sets, called L2-convex sets, is an intriguing object that is closely related to polymatroid intersection.…

Let $F$ be a locally compact non-Archimedean field, and $\bf G$ a connected quasi-split reductive group over $F$. We are interested in complex irreducible smooth generic representations $\pi$ of ${\bf G}(F)$. When $F$ has positive…

We show that ABV-packets for $p$-adic groups do not depend on the choice of a Whittaker datum, but the function from the ABV-packet to representations of the appropriate microlocal equivariant fundamental group does, and we find this…

Motivated by the Langlands program in representation theory, number theory and geometry, the theory of representations of a reductive $p$-adic group over a coefficient ring different from the field of complex numbers has been widely…

We extend the results by R.P. Langlands on representations of (connected) abelian algebraic groups. This is done by considering characters into any divisible abelian topological group. With this we can then prove what is known as the…

Following I. S. Krasilshchik and A. M. Vinogradov, we regard PDEs as infinite-dimensional manifolds with involutive distributions and consider their special morphisms called differential coverings, which include constructions like Lax pairs…

The geometric conjecture developed by the authors in [1,2,3,4] applies to the smooth dual Irr(G) of any reductive p-adic group G. It predicts a definite geometric structure - the structure of an extended quotient - for each component in the…

Focusing on the discrete probabilistic setting we generalize the combinatorial definition of cumulants to L-cumulants. This generalization keeps all the desired properties of the classical cumulants like semi-invariance and vanishing for…

Bernstein blocks of complex representations of p-adic reductive groups have been computed in a large amount of examples, in part thanks to the theory of types a la Bushnell and Kutzko. The output of these purely representation-theoretic…

In this paper, we give a uniform classification of the generic dual of quasi-split classical groups, their similitude counterparts, and general spin groups. As applications, for quasi-split classical groups, we show that the functorial…

Given a reductive group scheme $G$, we give a linear algebraic description of reduced \'etale $4$-cocycles on its classifying stack $\mathrm B(G)$. These cocycles form a $2$-groupoid, which we interpret as parameters of metaplectic covers…

We establish the endoscopic character identity for bounded $A$-packets of non-quasisplit even special orthogonal groups, with respect to elliptic endoscopic triples. The proof reduces the non-quasisplit case to the quasisplit case and the…

In this paper we show three new results concerning dimension datum. Firstly, for two subgroups $H_{1}$($\cong U(2n+1)$) and $H_{2}$($\cong Sp(n)\times SO(2n+2)$) of $SU(4n+2)$, we find a family of pairs of irreducible representations…

In this paper we use the concept of wavelet sets as introduced by X. Dai and D. Larson, to decompose the wavelet representation of the discrete group associated to an arbitrary $n \times n$ integer dilation matrix as a direct integral of…

We construct an endoscopic decomposition for local L-packets associated to irreducible cuspidal Deligne-Lusztig representations. Moreover, the obtained decomposition is compatible with inner twistings.

In this joint introduction to an Asterisque volume, we give a short discussion of the historical developments in the study of nonlinear covering groups, touching on their structure theory, representation theory and the theory of automorphic…